Find the variance and standard deviation of the data set to the nearest hundredth, if necessary. $0,1,4,9,36$
A) standard deviation: $10$ variation: $4$
B) standard deviation: $10$ variation: $178.8$
C) standard deviation: $178.8$ variation: $178.8$
D) standard deviation: $13.37$ variation: $178.8$
E) standard deviation: $13.37$ variation: $10$

Question

Quizplus · Accepted Answer

To find the variance, we must first find the mean of the data set:

$$\frac{0+1+4+9+36}{5}=10$$

Next, we find the deviation of each data point from the mean, square it and find the average:

$$(0-10)^2=100$$

$$(1-10)^2=81$$

$$(4-10)^2=36$$

$$(9-10)^2=1$$

$$(36-10)^2=676$$

$$\frac{100+81+36+1+676}{5}=178.8$$

Therefore, the variance is 178.8.

To find the standard deviation, we take the square root of the variance:

$$\sqrt{178.8}=13.37$$

Therefore, the standard deviation is 13.37. The correct choice is D.

Find the Variance and Standard Deviation of the Data Set 0,1,4,9,360,1,4,9,360,1,4,9,36

Find the Variance and Standard Deviation of the Data Set $0,1,4,9,36$